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A267711 Numbers n such that n (mod 3) = n (mod 5). 2
0, 1, 2, 15, 16, 17, 30, 31, 32, 45, 46, 47, 60, 61, 62, 75, 76, 77, 90, 91, 92, 105, 106, 107, 120, 121, 122, 135, 136, 137, 150, 151, 152, 165, 166, 167, 180, 181, 182, 195, 196, 197, 210, 211, 212, 225, 226, 227, 240, 241, 242, 255, 256, 257, 270, 271, 272, 285, 286 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Periodic differences between the consecutive terms (1,1,13,1,1,13,1,1,13,1,1...).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

a(n) = 1/3*(15*n-12*cos((2*pi*n)/3)+4*sqrt(3)*sin((2*pi*n)/3)-27).

G.f.: x^2*(13*x^2+x+1) / ((x-1)^2*(x^2+x+1)).

a(n) = a(n-1)+a(n-3)-a(n-4) for n>4. - Colin Barker, Jan 28 2016

MATHEMATICA

Select[ Range[0, 10000], (Mod[#, 3] == Mod[#, 5]) &]

PROG

(PARI) lista(nn) = for(n=0, nn, if(n%3 == n%5, print1(n, ", "))); \\ Altug Alkan, Jan 19 2016

(PARI) concat(0, Vec(x^2*(1+x+13*x^2)/((1-x)^2*(1+x+x^2)) + O(x^100))) \\ Colin Barker, Jan 28 2016

CROSSREFS

Cf. A267540.

Sequence in context: A322149 A163480 A037312 * A108472 A039771 A032934

Adjacent sequences:  A267708 A267709 A267710 * A267712 A267713 A267714

KEYWORD

nonn,easy

AUTHOR

Mikk Heidemaa, Jan 19 2016

STATUS

approved

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)